\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Apply the double-extraction technique of the Bolzano-Weierstrass proof to the sequence \(z_n = (-1)^n + i \cdot (-1)^{\lfloor n/2 \rfloor}\) for \(n \ge 0\). Exhibit a convergent subsequence.
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